In the simulations, we consider that the distance between the user and the RIS is \(d_{UI}=20\)  m, and the distance between the RIS and the BS is \(d_{IB}=700\)  m.
The distance between the user and the BS can be calculated from the geometric relationship as \(\left(d_{k}^{\mathrm {UB}}\right)^{2}=\left(d_{\mathrm {IB}}-d_{\mathrm {UI}} \sin \left(\frac{\pi }{5} \right)\right)^{2}+\left(d_{\mathrm {UI}} \cos \left(\frac{\pi }{5} \right)\right)^{2}\) .
With the distances, large-scale factors are set to \( \alpha _{k}=10^{-3} d_{\mathrm {UI}}^{-2} \) , \( \beta =10^{-3} d_{\mathrm {IB}}^{-2.5} \)  and \(\gamma _{k}=10^{-3}\left(d_{k}^{\mathrm {UB}}\right)^{-4}\) . Besides, we set \(M=N=64\) , \(p=30\)  dBm, \(\sigma ^2=-104\)  dBm, \(\tau _{c}=196\)[1]}, \(\tau =1\) , \(\delta =1\)  and \(\varepsilon _{k}=10\) .
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